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Chapter 32: Problem 13

The interference pattern from two slits separated by \(0.37 \mathrm{mm}\) has bright fringes with angular spacing \(0.065^{\circ} .\) Find the light's wavelength.

Short Answer

Expert verified
The wavelength of the light is approximately \(6.6 \times 10^{-7} \mathrm{m}\) or \(660 \mathrm{nm}\)

Step by step solution

01

Identify the Given Variables

The problem provides the distance between the slits as \(d = 0.37 \mathrm{mm} = 0.37 \times 10^{-3} \mathrm{m}\), and the angular spacing of the bright fringes as \(\Delta \theta = 0.065^{\circ} = 0.065 \times \frac{\pi}{180} \mathrm{rad}\), which have both been converted to SI units for consistency.
02

Apply the Double-Slit Diffraction Formula

The formula for double-slit diffraction is \(\lambda = d \cdot \sin(\Delta \theta)\) where \(\lambda\) is the wavelength of light to be found. This formula is true for the first order of light (m=1).
03

Calculate the Wavelength

Plugging the given values into the formula: \(\lambda = d \cdot \sin(\Delta \theta) = 0.37 \times 10^{-3} \mathrm{m} \cdot \sin(0.065 \times \frac{\pi}{180} \mathrm{rad})\)

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Most popular questions from this chapter

A proposed "star wars" antimissile laser is to focus infrared light with 2.8 -\mum wavelength to a 50 -cm-diameter spot on a missile \(2500 \mathrm{km}\) distant. Find the minimum diameter for a concave mirror that can achieve this spot size, given the diffraction limit. (Your answer suggests one of many technical difficulties faced by antimissile defense systems.)

For a double-slit system with slit spacing \(0.0525 \mathrm{mm}\) and wavelength \(633 \mathrm{nm},\) at what angular position is the path difference a quarter wavelength?

One arm of a Michelson interferometer is \(42.5 \mathrm{cm}\) long and is enclosed in a box that can be evacuated. The box initially contains air, which is gradually pumped out. In the process, 388 bright fringes pass a point in the viewer. If the interferometer uses light with wavelength \(641.6 \mathrm{nm},\) what's the air's refractive index?

A double-slit experiment has slit spacing \(0.12 \mathrm{mm}\). (a) What should be the slit-to-screen distance \(L\) if the bright fringes are to be \(5.0 \mathrm{mm}\) apart when the slits are illuminated with 633 -nm laser light? (b) What will be the fringe spacing with 480 -nm light?

A thin-walled glass tube of length \(L\) containing a gas of unknown refractive index is placed in one arm of a Michelson interferometer using light of wavelength \(\lambda\). The tube is then evacuated. During the process, \(m\) bright fringes pass a fixed point in the viewer. Find an expression for the refractive index of the gas.
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